Q: What is the total or count of factors of the number 216,526,401?

A: 48

How do I find the total factors of the number 216,526,401?

Step 1

Find the prime factorization of the number 216,526,401.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree

	216,526,401

3		72,175,467

	3		24,058,489

		7		3,436,927

			13		264,379

				59		4,481

The prime factorization in exponential form is: 3² x 7¹ x 13¹ x 59¹ x 4,481¹

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

216,526,401 = 3² x 7¹ x 13¹ x 59¹ x 4,481¹

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)

d(216526401) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(216526401) = (3)(2)(2)(2)(2)

d(216526401) = 48

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Take a look at the factors page to see the factors of 216,526,401 and how to find them.

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